Question

If the numerator and denominator of a fraction are increased by 2 and 1 respectively it becomes 3/4, if the numerator and denominator are decreased by 2 and 1 respectively it becomes 1/2. find the fraction

Answer 1

Answer: 7/11

Step-by-step explanation:

Let the numerator be x and denominator be y.

(x + 2) ÷ (y + 1) = 3/4

Cross multiplication

4 (x + 2) = 3 (y + 1)

4x + 8 = 3y + 3

4x - 3y = -5 → ①

(x - 2) ÷ (y - 1) = 1/2

Cross multiplication

2 (x - 2) = y - 1

2x - 4 = y - 1

2x - y = 3. → ②

Multiply eqn ① by 1 and eqn ② by 2

Eqn ① by 1 - 4x - 3y = -5

Eqn ② by 2 - 4x -2y = 6

Subtract eqn ② from eqn ①

4x - 3y - 4x + 2y = -5 - 6

-y = -11

y = 11

Sub y = 11 in eqn ②

2x - 11 = 3

2x = 14

x = 7

Fraction = x/y = 7/ 11

Answer 2

Answer:

fraction=x/y=7/11

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